A Polynomial Algorithm for Checking Diagnosability of Petri Nets

We consider decentralized diagnosis in discrete event systems that are modeled as non-deterministic finite automata and are observed, through distinct natural projection maps, at multiple observation sites. Specifically, we consider a scenario where two or more observers (each with its own map) are allowed to communicate their assessments (state estimates and matching normal/failure conditions) to a centralized location which then makes an overall decision based on the intersection of the local state estimates and their matching conditions. This intersection based decentralized diagnosis (IBDD) scheme can be implemented with polynomial complexity, both at the observation sites and at the centralized location. It is shown that IBDD can be verified with an algorithm of polynomial complexity that constructs verifiers for the observation sites, and analyzes properties of their parallel composition and product with the system.

In this paper a new approach to fault diagnosis of discrete events systems modeled with Petri nets is presented. Fault events are associated to a subset of unobservable transitions of the net. Negative markings, called generalized marking, are used to estimate the explanations of the observed transitions. The generalized markings allow to cope with the problems related with the explosion of the state space estimation in a very efficient way in terms of memory usage. This feature makes the proposed approach suitable for the on-line fault diagnosis of discrete event systems.

Recently, safe diagnosability of discrete event systems (DESs) was investigated by Paoli and Lafortune, which was viewed as the first necessary step of fault-tolerant supervision. In this paper, we consider the problem of safe diagnosability in the framework of stochastic discrete event systems (SDESs). We define the notion of safe diagnosability for stochastic automata, in which fault detection occurs before any given forbidden string in the failed mode of system is executed. The relationship between diagnosability and safe diagnosability for SDESs is analyzed. In particular, a necessary and sufficient condition for safe diagnosability of SDESs is presented by constructing the recognizer of illegal language and the safe diagnoser. Some examples are described to illustrate the results.

The aim of diagnosis is to detect and isolate faults according to the observable traces generated by the system. This article concerns multi-steps diagnosis of discrete event systems modelled with ordinary Petri nets. The main contribution is to decide which sets of places must be considered for r-steps diagnosis of some fault transitions or groups of fault transitions. Conditions and algorithms are proposed that lead to sensor selection in order to design diagnosers in a systematic way without expanding the reachability graph of the Petri net models.

The problem of safe failure diagnosis in discrete event systems is addressed. Starting from the standard definition of diagnosability of discrete event systems, which deals with the problem of detecting the occurrence of an unobservable event using the available observations on the system, the problem of performing the detection before the system executes a forbidden string is introduced. For example, this constraint could be required to prevent local faults from developing into failures that could cause safety hazards. This idea results in a new language property for discrete event systems called safe diagnosability. Necessary and sufficient conditions to test this language property are presented. Moreover, the problem of explicitly taking into account safe diagnosability as a requirement in system design is discussed.

formula omitted]-diagnosability for active on-line diagnosis in discrete event systems

Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

This paper is about the fault diagnosis of discrete event systems (DES) under time constraints. The DES contains a series of tasks with well-defined time intervals for each, collected during repetitive runs of the system. The repetitive runs allowed us to calculate average function time for each task. The objective is to propose an algorithm that verifies the correct behavior of each individual task within the system. To illustrate the principal of the algorithm, we will apply it with two concrete examples. This algorithm is easy to implement and operate, and is very useful for all types of systems.

This paper addresses fault pattern diagnosis of discrete event systems, involving fault pattern detection and diagnosability. A fault pattern is modelled as a finite automaton whose accepted language is the objective to be diagnosed, representing the occurrence of complex or composite faults. A verifier for fault pattern detection based on the synchronous product of a system and a fault pattern is proposed. By removing all silent events, a silent closure is calculated based on the synchronous product, which offers computational advantages for systems that have a large number of silent events. An NSC/FSC pair verifier is then computed by taking the product of a normal silent closure and an accepted silent closure. By studying indeterminate cycles of the NSC/FSC pair verifier, necessary and sufficient verification conditions are established, asserting that a system is diagnosable with respect to a fault pattern if and only if there is no indeterminate cycle in the NSC/FSC pair verifier. It is shown that the proposed method requires polynomial time at most. Finally, a case study to illustrate the results is provided.

Diagnosability is an important property in the field of fault diagnosis. In this paper, a novel approach based on logical formula is proposed to verify diagnosability of Discrete event systems(DESs). CNFFSM is defined to represent a new model for DES. Each transition in DES can be described as a clause. According to CNF-FSM, we construct a CNF-diagnoser. Based on the resolution principle and CNF-diagnoser, an algorithm is presented to test whether the failure events can be detected or not in a finite number of observable events. Our algorithm can be applied in both off-line diagnosis and on-line diagnosis. Experimental results show that our algorithm can solve the diagnosability problem efficiently.

In the conventional framework for failure diagnosis of partially observed discrete event systems, it is assumed that, for each event, the corresponding output symbol is determined uniquely. However, this assumption does not hold in discrete event systems such as a mobile system, where an output symbol depends on not only an event but also a state at which the event occurs. In this paper, we model such discrete event systems by Mealy automata with nondeterministic output functions, and consider a decentralized failure diagnosis problem that requires any occurrence of a failure should be detected by at least one local diagnoser within a uniformly bounded number of steps. We present a necessary and sufficient condition for the existence of a decentralized diagnoser. We then present an algorithm for verifying this condition. Moreover, we present a method for synthesizing local online diagnosers.

Generalized Robust Diagnosability of Discrete Event Systems

This paper addresses the problem of online fault detection and diagnosis in discrete event systems modeled by labeled Petri nets and using Integer Linear Programming Problem (ILPP) solutions. In particular, unobservable (silent) transitions model faults and both observable and unobservable transitions model the nominal system behavior. Furthermore, observable transitions exhibit a kind of non determinism since several different transitions may share the same event label. This paper proposes two diagnosers that work in two different system settings. The first one is a centralized fault detection strategy: the diagnoser waits for an observable event and an algorithm defines and solves some ILPPs to decide whether the system behavior is normal or may exhibit some faults. In the second setting, the system consists of a set of interacting PN modules and each module is monitored by a diagnoser that has local information on the module structure. Moreover, each diagnoser observes and detects the faults of the module it is attached to and shares information in some of its places that are shared with other modules of the system. Some case studies show the two different approaches and point out the peculiarities of the proposed strategies.

We are interested in constructing monitors for the detection of confidential information flow in the context of partially observable discrete event systems. We focus on the case where the secret information is given as a regular language. We first characterize the set of observations allowing an attacker to infer the secret information. Further, based on the diagnosis of discrete event systems, we provide necessary and sufficient conditions under which detection and prediction of secret information flow can be ensured, and construct a monitor allowing an administrator to detect it.

We consider a reliable decentralized diagnosis problem for discrete event systems in the inference-based framework. This problem requires us to synthesize local diagnosers such that the occurrence of any failure string is correctly detected within a finite number of steps, even if local diagnosis decisions of some local diagnosers are not available. In the case of single-level inference, we introduce a notion of reliable 1-inference-diagnosability and show that reliable 1-inference-diagnosability is a necessary and sufficient condition for the existence of a solution to the reliable decentralized diagnosis problem. Then, we show how to verify reliable 1-inference-diagnosability effectively. When the system to be diagnosed is reliably 1-inference-diagnosable, we compute the delay bound within which the occurrence of any failure string can be detected. Local diagnosers can be constructed using the computed delay bound.